Relations in Grassmann Algebra Corresponding to Three- and Four-Dimensional Pachner Moves
New algebraic relations are presented, involving anticommuting Grassmann variables and Berezin integral, and corresponding naturally to Pachner moves in three and four dimensions. These relations have been found experimentally – using symbolic computer calculations; their essential new feature is th...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2011 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2011
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/148082 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Relations in Grassmann Algebra Corresponding to Three- and Four-Dimensional Pachner Moves / I.G. Korepanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 17 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862747526086524928 |
|---|---|
| author | Korepanov, I.G. |
| author_facet | Korepanov, I.G. |
| citation_txt | Relations in Grassmann Algebra Corresponding to Three- and Four-Dimensional Pachner Moves / I.G. Korepanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 17 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | New algebraic relations are presented, involving anticommuting Grassmann variables and Berezin integral, and corresponding naturally to Pachner moves in three and four dimensions. These relations have been found experimentally – using symbolic computer calculations; their essential new feature is that, although they can be treated as deformations of relations corresponding to torsions of acyclic complexes, they can no longer be explained in such terms. In the simpler case of three dimensions, we define an invariant, based on our relations, of a piecewise-linear manifold with triangulated boundary, and present example calculations confirming its nontriviality.
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| first_indexed | 2025-12-07T20:51:39Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148082 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T20:51:39Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Korepanov, I.G. 2019-02-16T20:46:53Z 2019-02-16T20:46:53Z 2011 Relations in Grassmann Algebra Corresponding to Three- and Four-Dimensional Pachner Moves / I.G. Korepanov // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 17 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 15A75; 55-04; 57M27, 57Q10; 57R56 DOI: http://dx.doi.org/10.3842/SIGMA.2011.117 https://nasplib.isofts.kiev.ua/handle/123456789/148082 New algebraic relations are presented, involving anticommuting Grassmann variables and Berezin integral, and corresponding naturally to Pachner moves in three and four dimensions. These relations have been found experimentally – using symbolic computer calculations; their essential new feature is that, although they can be treated as deformations of relations corresponding to torsions of acyclic complexes, they can no longer be explained in such terms. In the simpler case of three dimensions, we define an invariant, based on our relations, of a piecewise-linear manifold with triangulated boundary, and present example calculations confirming its nontriviality. This paper has been written with partial financial support from Russian Foundation for Basic
 Research, Grant no. 10-01-00088-a, and a grant from the Academic Senate of Moscow State
 University of Instrument Engineering and Computer Sciences. I also thank the referees for their constructive and helpful comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Relations in Grassmann Algebra Corresponding to Three- and Four-Dimensional Pachner Moves Article published earlier |
| spellingShingle | Relations in Grassmann Algebra Corresponding to Three- and Four-Dimensional Pachner Moves Korepanov, I.G. |
| title | Relations in Grassmann Algebra Corresponding to Three- and Four-Dimensional Pachner Moves |
| title_full | Relations in Grassmann Algebra Corresponding to Three- and Four-Dimensional Pachner Moves |
| title_fullStr | Relations in Grassmann Algebra Corresponding to Three- and Four-Dimensional Pachner Moves |
| title_full_unstemmed | Relations in Grassmann Algebra Corresponding to Three- and Four-Dimensional Pachner Moves |
| title_short | Relations in Grassmann Algebra Corresponding to Three- and Four-Dimensional Pachner Moves |
| title_sort | relations in grassmann algebra corresponding to three- and four-dimensional pachner moves |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148082 |
| work_keys_str_mv | AT korepanovig relationsingrassmannalgebracorrespondingtothreeandfourdimensionalpachnermoves |